학술저널
THE STUDY OF THE SYSTEM OF NONLINEAR WAVE EQUATIONS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 20, No. 3
-
2007.09261 - 267 (7 pages)
- 0
We show the existence of the positive solution for the system of the following nonlinear wave equations with Dirichlet boundary conditions utt ¡ uxx + av+ = sÁ00 + f; vtt ¡ vxx + bu+ = tÁ00 + g;u(§¼2; t) = v(§¼2; t) = 0;where u+ = maxfu; 0g, s, t 2 R, Á00 is the eigenfunction cor-responding to the positive eigenvalue ¸00 = 1 of the eigenvalue problem utt ¡ uxx = ¸mnu with u(§¼2 ; t) = 0, u(x; t + ¼) =u(x; t) = u(¡x; t) = u(x;¡t) and f, g are ¼-periodic, even in xand t and bounded functions in [¡¼2 ; ¼2 ]£[¡¼2 ; ¼2 ] withR ¼2¡¼2fÁ00 =R ¼2¡¼2gÁ00 = 0.
1. Introduction and statement of main result
2. Proof of Theorem 1.1
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